SOLUTION: At a large factory, the employees were surveyed and classified according to their level of education and whether they smoked. The data are shown in the table. Educational level

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Question 1160641: At a large factory, the employees were surveyed and classified according to their level of education and whether they smoked. The data are shown in the table.
Educational level
Not high school Graduate
6 students smoke
18 do not smoke
High school graduate
14 smoke
7 do not smoke
College Graduate
19 smoke
25 do not smoke


If an employee is selected at random, find these probabilities.
a. The employee smokes, given that he or she graduated from college.
b. Given that the employee did not graduate from high school, he or she is a smoker
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

There is a fallacy here because you must be a high school graduate if you are a
college graduate.  So when you speak of high school graduates are you including
the college graduates too?  I'm guessing not.

I will assume that when you say "high school graduate" you mean "high school
graduate only, not a college graduate". 

Anyway we'll use the reduced sample space method for conditional probability.
a. The employee smokes, given that he or she graduated from college.
Reduce the sample space to what is given, the 19+25=44 college graduates:

That's 19/44 = 0.43 approximately.
b. Given that the employee did not graduate from high school, he or she is a smoker
Reduce the sample space to what is given, the 6+19=24 that did not graduate from
high school:

That's 6/24 = 1/4 = 0.25

Edwin